MATHEMATICS-III (Aditya Publication)
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Unit I: Ordinary Differential Equations: Complete solution, Operator D, rules for finding the complementry function, the inverse operator, Rules for finding particular integral. Method of variation of parameters, Cauchy's and Legendre's Linear Differential equations. Simultaneous linear differential equations with constant coefficients Applications to civil engineering.
Unit II: Laplace Transforms: Definition and elementry properties, Inverse L.T. by various methods, Convolution theorem, Solution of ordinary differential equation using Laplace transform of periodic functions. Application to problems of beams and fluids.
Unit III: Partial Differential Equations: P.D.E. of first order and first degree of types i) f(p,q) = O ii) f(p,q,z)=0, iii) f(p,q,x,y)=O iv) f(p,q,x,y,z)=O i.e. (a) Lagrange's form Pp + Qq = R (b) Clairtut's form z=px+qy+f(p,q) v) Equations reducible to above standard types linear Homogeneous P.D.E. of nth order with constant coefficients.
Unit IV: Numerical Methods: (i) Solution of Algebraic and transcendal Equations by Newton Raphson method and by method of False Position. (ii) Solution of system of linear equations by Grout's method, Gauss Seidal method and Relaxation Method. Numerical solution of differential equations by Picard's method, Taylor's series method, Euler's method, modified Euler's method and Rungekutta forth order method.
Unit V: Complex Variable: Analytic functions, C.R.conditions, Harmonic functions. harmonic conjugate functions, Milne's method, conformal mappings (translation, rotation, magnification, inversion, bilinear transformation).
Unit VI: Statistics: Probability: Axioms, conditional probability, Baye's theorem, Mathematical Expectation and probability distributions (Binomial, Poisson and Normal). Curve fitting by method of least square only for line and parabola, Correlation, regression.
|Category||Books - Engineering - Civil - Semester-III|
|Dimensions||10(l) * 1(w) *10(h) CM|